There are three different birthstones associated with the month of December: Blue Topaz, Turquoise and Tanzanite. All three birthstones vary in its properties but have one thing common i.e its unique blue color.

Blue Topaz

Blue Topaz, a variation of the most common gem Topaz, is the birthstone for the month of December. The name "Topaz" is derived from the Greek word "Topazos". Topaz is a silicate mineral of aluminum and fluorine that is found in pegmatites near silica rock that are volcanic in origin.
There are three main shades of Blue Topaz: London Blue, Sky and Swiss. London Blue is the deepest of blue and it is a substitute to Sapphire for those who cannot afford.
Ancient traditional birthstones:

Arabic: Ruby

Guardian angel: Adnachiel

Hebrew: Ruby

Hindu: Topaz

His Talismanic stone: Beryl

Polish: Turquoise

Roman: Ruby

When gifted to a loved one, the blue topaz symbolizes eternal love and faithfulness.

Turquoise

The word Turquoise is derived from the Greek word "Turkois" which means "Turkish"; it is so called because it was first brought from Turkey. Turquoise is a mineral consisting of copper aluminum phosphate. Turquoise is the only gemstone belonging to the phosphates family. Turquoise is found in the following countries: Iran, United States, Africa, Australia, Siberia, and Europe.
Turquoise is the Wedding anniversary gemstone for the 5th and 11th year of marriage. Turquoise is symbol of happiness, success and good fortune for those born in the month of December.

Tanzanite

This extraordinary gemstone was discovered in 1967 was enthusiastically celebrated by the specialists as the 'gemstone of the 20th century'. It is named after the East African state of Tanzania, the only place in the world where it has been found.
Tanzanite is blue, surrounded by a fine hint of purple. It consists of calcium aluminium silicate and is not particularly hard, having a value of 6.5 to 7 on the Mohs scale.